Transient behavior of the Halfin-Whitt diffusion

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

van Leeuwaarden, Johan S. H.^1,2  Knessl, Charles³ 

[1] Eindhoven Univ Technol, NL-5600 MB Eindhoven, Netherlands

[2] EURANDOM, NL-5600 MB Eindhoven, Netherlands

[3] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

关键词: GI/M/s queue;    M/M/s queue;    Halfin-Whitt regime;    Queues in heavy traffic;    Diffusion;    Asymptotic analysis;   

DOI  :  10.1016/j.spa.2011.03.007

来源: Elsevier

【 摘 要 】

We consider the heavy-traffic approximation to the GI/M/s queueing system in the Halfin-Whitt regime, where both the number of servers s and the arrival rate lambda grow large (taking the service rate as unity), with lambda = s - beta root s and beta some constant. In this asymptotic regime, the queue length process can be approximated by a diffusion process that behaves like a Brownian motion with drift above zero and like an Ornstein-Uhlenbeck process below zero. We analyze the transient behavior of this hybrid diffusion process, including the transient density, approach to equilibrium, and spectral properties. The transient behavior is shown to depend on whether beta is smaller or larger than the critical value beta(*) approximate to 1.85722, which confirms the recent result of Gamarnik and Goldberg (2008) [8]. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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